Theorem mulcomi 8228

Description: Commutative law for multiplication. (Contributed by NM, 23-Nov-1994.)

Hypotheses

Ref	Expression
axi.1	|- A e. CC
axi.2	|- B e. CC

Assertion

Ref	Expression
mulcomi	|- ( A x. B ) = ( B x. A )

Proof of Theorem mulcomi

Step	Hyp	Ref	Expression
1		axi.1	. 2 |- A e. CC
2		axi.2	. 2 |- B e. CC
3		mulcom 8204	. 2 |- ( ( A e. CC /\ B e. CC ) -> ( A x. B ) = ( B x. A ) )
4	1, 2, 3	mp2an 426	1 |- ( A x. B ) = ( B x. A )

Syntax hints:   = wceq 1398   e. wcel 2202  (class class class)co 6028   CCcc 8073   x. cmul 8080

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 108  ax-mulcom 8176

This theorem is referenced by:  mulcomli  8229  8th4div3  9405  numma2c  9700  nummul2c  9704  9t11e99  9784  binom2i  10956  fac3  11040  tanval2ap  12337  pockthi  12994  decsplit1  13064  decsplit  13065  sincosq4sgn  15623  2logb9irrALT  15768  2lgsoddprmlem2  15908  2lgsoddprmlem3d  15912